One of the main limitations of multirotor UAVs is their short flight time due to battery constraints. A practical solution for continuous operation is to power the drone from the ground via a tether. While this approach has been demonstrated for stationary systems, scenarios with a fast-moving base vehicle or strong wind conditions require modeling the tether forces, including aerodynamic effects. In this work, we propose two complementary approaches for real-time quasi-static tether modeling with aerodynamics. The first is an analytical method based on catenary theory with a uniform drag assumption, achieving very fast solve times below 1~ms. The second is a numerical method that discretizes the tether into segments and lumped masses, solving the equilibrium equations using CasADi and IPOPT. By leveraging initialization strategies, such as warm starting and analytical initialization, real-time performance was achieved with a solve time of 5~ms, while allowing for flexible force formulations. Both approaches were validated in real-world tests using a load cell to measure the tether force. The results show that the analytical method provides sufficient accuracy for most tethered UAV applications with minimal computational cost, while the numerical method offers higher flexibility and physical accuracy when required. These approaches form a lightweight and extensible framework for real-time tether simulation, applicable to both offline optimization and online tasks such as simulation, control, and trajectory planning.

翻译：多旋翼无人机的主要局限之一在于电池约束导致的短续航时间。一种实现持续运行的实用方案是通过系绳从地面为无人机供电。尽管该方法已在静态系统中得到验证，但在基础载体快速移动或强风条件下，需要对包含空气动力学效应的系绳力进行建模。本研究提出了两种互补的实时准静态系绳空气动力学建模方法。第一种是基于悬链线理论并采用均匀阻力假设的解析方法，求解时间低于1毫秒。第二种是数值方法，将系绳离散为分段和集中质量，利用CasADi和IPOPT求解平衡方程。通过采用热启动与解析初始化等策略，在实现5毫秒求解时间的同时保持了实时性能，并支持灵活的力表述形式。两种方法均通过使用测力传感器测量系绳力的实际测试进行验证。结果表明：解析方法能以最小计算成本为大多数系留无人机应用提供足够精度，而数值方法在需要时可提供更高的灵活性与物理精度。这些方法构成了轻量级可扩展的实时系绳仿真框架，适用于离线优化及仿真、控制与轨迹规划等在线任务。